There are many things that could have gone
really wrong with a book like this. The good news is that none of them did.
Things could have gone really wrong because this is a book about computation
that is also a novel, and moreover a novel that contains both an international
cyber-intrigue and a fair amount of intellectual history. If that sounds like
a recipe for confusion to you, then you share the worries I had when I began to
read this book. But despite the occasional sense that things weren't quite
holding together, when I finished the book I came away entertained and
impressed by what the author pulled off.

The reader of this review should know something
about the reviewer. As I am a logician, specializing in the theory of
computation and having studied the history and philosophy of science, there was
not a whole lot new for me about computation or intellectual history in this
book. But despite this, I thoroughly enjoy reading what Papadimitriou wrote
about these topics, and seeing them from his perspective. Speaking of his
perspective, the reader of this review should also know that Papadimitriou is a
very distinguished computer scientist, and a noted expert in the theory of
computation. His presentation of the theory of computation is both masterful
(no surprise) and pleasantly light-handed (also not a surprise for those who
have read his technical work). Anyone who wants to learn about what
computation really is, but does not want to get into the trenches with Turing
machines and complexity classes, will not go wrong reading this novel. There
is a lot of muddled thinking about computation, and much nonsense written about
it in popular books. Much of this stems from the inability to distinguish
computation, and what it can and cannot do, from the handy devices we all use
to send email and shop online. While these machines are fun, useful and have
transformed our society in a remarkably short time, the beauty and power of
computation is usually lost on all but the few who study it seriously.
Papadimitriou brings some of that beauty and power to the non-expert.

But as I said, this book is also a novel. The
main live, human characters are Alexandros, an archaeologist, Ethel, an
extremely successful computer executive, and Ian, an uber-hacker. The main
historical character is Alan Turing, the mathematician who played such a key
role in establishing what computation is, and what it can and cannot do. There
is also a character named Turing who is a very special sort of computer program
that Alexandros makes contact with, and that teaches him all of the lessons in
computation and science that I have mentioned. But Turing-the-program is more
than a tutor, he ends up being a key player in the cyber-intrigue that is
developed around Ethel and Ian, and that draws in Alexandros. Of these various
characters, the most interesting are Alexandros and the historical Alan Turing.
Alexandros is an expert in archeology, but starts out knowing nothing about
computation and its related subjects. His intellectual capabilities and
technical naïveté make him the perfect tutee for Turing-the-program. But there
is also a love story that Alexandros is a main player in, and it is his
character's development in that love story that is the most successful
novelistic feature of the book.

The historical Turing was a profound thinker,
whose deeply important mathematics had the extremely rare consequence of
quickly changing the world we live in. He did this not only with his work on
computation, but also his contributions to cryptanalysis during the Second
World War. But Turing was also man whose life ended when he was still young.
Because he was a homosexual, Turing was badgered and eventually persecuted by
the authorities in his own country, England. This led him to take his own life.
Papadimitriou tells Turing's story very well, and it brings home the sadness of
his life and the senseless loss of a great talent.

The cyber-intrigue centered on Ian and Ethel is
the least successful part of the book. Perhaps the dotcom collapse has taken
the bloom off the virtual rose, but when we move from the sand and sun world of
Alexandros and the moving story of Turing to the tale of Ian and his hacking
exploits the novel loses some of its energy and drive. But this is really a
minor complaint, and I am willing to admit that it may well stem from my
general dislike of science fiction, or anything that even smells like it. And
the cyber-intrigue has a bit of that scent.

If you want an entertaining book that teaches
you a lot about the theory of computation, that engages you in the humanness of
a great figure from history and that tells an often compelling tale about some
very interesting people, then this is a book for you.

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